Helser and Hayes: Quantitative management advice based on stock abundance indices 295 



management, or both. Given the data limitations for 

 wolffish, what value will serve as a reasonable refer- 

 ence point or proxy for a level of stock abundance 

 below which the stock may be in jeopardy? For our 

 example we chose the lower quartile of the fitted 

 survey abundance indices for wolffish as a reference 

 point. Admittedly the choice of a computed statistic 

 and the period of years of the survey indices used 

 are rather arbitrary; the situation for each species 

 should be carefully considered and a suitable refer- 

 ence point agreed upon by fishery managers. How- 

 ever, no matter which reference point is used, a 

 simple comparison of a survey index in any given 

 year with a survey-based reference point fails to con- 

 sider the variability in each of these quantities. 



Results and discussion 



Estimates of the stratified mean number per tow 

 (transformed by natural logarithms) clearly show 

 declining trends in abundance, and the fitted index 

 derived from time-series analysis appeared to pro- 

 vide a good, and less variable, representation of the 

 observed data (Fig. 4). The maximum likelihood es- 

 timate of the integrated moving average parameter 

 (0) was 0.50 [SE( 0)=O.2O], although it is probably not 

 reliably estimated as indicated by the relatively flat 

 maximum likelihood surface between and 0.6. 



Survey indices 

 Observed 



Fitted 



Year 



Figure 4 



Predicted indices derived from an integrated moving aver- 

 age model fitted to observed Atlantic wolffish, Anarhichas 

 lupus, spring bottom trawl survey indices (log e [stratified 

 mean number per tow]) from 1968 to 1992. Predicted indi- 

 ces are compared to the lower quartile (25th percentile) of 

 1968-92 fitted indices as an arbitrary chosen reference point. 



